BRITISH STANDARD BS EN EN 1993-1-1:2005 1993-1-1:2005 Incorporating +A1:2014 Eurocode 3: Design of steel structures — Part 1-1: General rules and rules for buildings ICS 91.010.30; 91.080.10 Corrigenda Incorporating February 2006 Corrigenda and April2006 2009 February and April 2009 BS EN 1993-1-1:2005+A1:2014 National foreword This British Standard is the UK implementation of EN 1993-1-1:2005+A1:2014, incorporating corrigenda February 2006 and April 2009 It supersedes BS EN 1993-1-1:2005, which is withdrawn The start and finish of text introduced or altered by corrigendum is indicated in the text by tags Tags indicating changes to CEN text carry the number of the CEN corrigendum For example, text altered by February 2006 corrigendum is indicated by The start and finish of text introduced or altered by amendment is indicated in the text by tags Tags indicating changes to CEN text carry the number of the CEN amendment For example, text altered by CEN amendment A1 is indicated by Where a normative part of this EN allows for a choice to be made at the national level, the range and possible choice will be given in the normative text, and a note will qualify it as a Nationally Determined Parameter (NDP) NDPs can be a specific value for a factor, a specific level or class, a particular method or a particular application rule if several are proposed in the EN To enable BS EN 1993-1-1:2005+A1:2014 to be used in the UK the latest version of the NA to this Standard containing these NDPs should also be used At the time of publication, it is NA+A1:2014 to BS EN 1993-1-1:2005+A1:2014 BSI, as a member of CEN, is obliged to publish EN 1993-1-1:2005+A1:2014 as a British Standard However, attention is drawn to the fact that during the development of this amendment to this European Standard, the UK committee voted against its approval The UK voted against its approval due to objections to the technical content of Annex C relating to the achievement of structural reliability These objections have largely been addressed in the UK decisions on C.2.2 (3) and C.2.2 (4) in the NA+A1:2014 to BS EN 1993-1-1:2005+A1:2014 The UK participation in its preparation was entrusted to Technical Committee CB/203, Design & execution of steel structures A list of organizations represented on this committee can be obtained on request to its secretary This publication does not purport to include all the necessary provisions of a contract Users are responsible for its correct application Compliance with a British Standard cannot confer immunity from legal obligations This British Standard was published under the authority of the Standards Policy and Strategy Committee on 18 May 2005 © The British Standards Institution 2015 Published by BSI Standards Limited 2015 ISBN 978 580 83130 Amendments/corrigenda issued since publication Amd No Date 16568 29 September 2006 Implementation of CEN corrigendum February 2006 Corrigendum No Comments 28 February 2010 Implementation of CEN corrigendum April 2009 30 June 2015 Implementation of CEN amendment A1:2014 EN EN 1993-1-1 1993-1-1:2005+A1 EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM May May 2005 2014 ICS 91.010.30; 91.080.10 Supersedes ENV 1993-1-1:1992 Incorporating Corrigenda February 2006 and March 2009 English version Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings Eurocode 3: Calcul des structures en acier - Partie 1-1: Règles générales et règles pour les bâtiments Eurocode 3: Bemessung und Konstruktion von Stahlbauten - Teil 1-1: Allgemeine Bemessungsregeln und Regeln für den Hochbau This European Standard was approved by CEN on 16 April 2004 CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the Central Secretariat or to any CEN member This European Standard exists in three official versions (English, French, German) A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the official versions CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom EUROPEAN COMMITTEE FOR STANDARDIZATION COMITÉ EUROPÉEN DE NORMALISATION EUROPÄISCHES KOMITEE FÜR NORMUNG Management Centre: rue de Stassart, 36 © 2005 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members B-1050 Brussels Ref No EN 1993-1-1:2005: E BS EN 1993-1-1:2005+A1:2014 BS 1993-1-1:2005 ENEN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) Contents Page General 1.1 Scope 1.2 Normative references 10 1.3 Assumptions 11 1.4 Distinction between principles and application rules 11 1.5 Terms and definitions 11 1.6 Symbols 12 1.7 Conventions for member axes 20 Basis of design 22 2.1 Requirements 22 2.1.1 Basic requirements 22 2.1.2 Reliability management 22 2.1.3 Design working life, durability and robustness 22 2.2 Principles of limit state design 23 2.3 Basic variables 23 2.3.1 Actions and environmental influences 23 2.3.2 Material and product properties 23 2.4 Verification by the partial factor method 23 2.4.1 Design values of material properties 23 2.4.2 Design values of geometrical data 23 2.4.3 Design resistances 24 2.4.4 Verification of static equilibrium (EQU) 24 2.5 Design assisted by testing 24 Materials 25 3.1 General 25 3.2 Structural steel 25 3.2.1 Material properties 25 3.2.2 Ductility requirements 25 3.2.3 Fracture toughness 25 3.2.4 Through-thickness properties 27 3.2.5 Tolerances 28 3.2.6 Design values of material coefficients 28 3.3 Connecting devices 28 3.3.1 Fasteners 28 3.3.2 Welding consumables 28 3.4 Other prefabricated products in buildings 28 Durability 28 Structural analysis 29 5.1 Structural modelling for analysis 29 5.1.1 Structural modelling and basic assumptions 29 2 BS EN 1993-1-1:2005+A1:2014 BS EN 1993-1-1:2005 EN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) 5.1.2 5.1.3 Joint modelling 29 Ground-structure interaction 29 5.2 Global analysis 30 5.2.1 Effects of deformed geometry of the structure 30 5.2.2 Structural stability of frames 31 5.3 Imperfections 32 5.3.1 Basis 32 5.3.2 Imperfections for global analysis of frames 33 5.3.3 Imperfection for analysis of bracing systems 36 5.3.4 Member imperfections 38 5.4 Methods of analysis considering material non-linearities 38 5.4.1 General 38 5.4.2 Elastic global analysis 39 5.4.3 Plastic global analysis 39 5.5 Classification of cross sections 40 5.5.1 Basis 40 5.5.2 Classification 40 5.6 Cross-section requirements for plastic global analysis 41 Ultimate limit states 45 6.1 General 45 6.2 Resistance of cross-sections 45 6.2.1 General 45 6.2.2 Section properties 46 6.2.3 Tension 49 6.2.4 Compression 49 6.2.5 Bending moment 50 6.2.6 Shear 50 6.2.7 Torsion 52 6.2.8 Bending and shear 53 6.2.9 Bending and axial force 54 6.2.10 Bending, shear and axial force 56 6.3 Buckling resistance of members 56 6.3.1 Uniform members in compression 56 6.3.2 Uniform members in bending 60 6.3.3 Uniform members in bending and axial compression 64 6.3.4 General method for lateral and lateral torsional buckling of structural components 65 6.3.5 Lateral torsional buckling of members with plastic hinges 67 6.4 Uniform built-up compression members 69 6.4.1 General 69 6.4.2 Laced compression members 71 6.4.3 Battened compression members 72 6.4.4 Closely spaced built-up members 74 Serviceability limit states 75 7.1 General 75 7.2 Serviceability limit states for buildings 75 7.2.1 Vertical deflections 75 7.2.2 Horizontal deflections 75 7.2.3 Dynamic effects 75 Annex A [informative] – Method 1: Interaction factors kij for interaction formula in 6.3.3(4) 76 3 BS EN 1993-1-1:2005+A1:2014 EN 1993-1-1:2005+A1:2014 (E) Annex B [informative] – Method 2: Interaction factors kij for interaction formula in 6.3.3(4)��������������79 Annex C (normative) Selection of execution class����������������������������������������������������������������������������������������������� 81 Annex AB [informative] – Additional design provisions�����������������������������������������������������������������������������83 Annex BB [informative] – Buckling of components of building structures�����������������������������������������������84 BS EN 1993-1-1:2005+A1:2014 BS BS EN EN 1993-1-1:2005 1993-1-1:2005 EN 1993-1-1:2005+A1:2014 EN 1993-1-1:2005 (E) (E) Foreword Foreword EN 1993-1-1:2005 (E) This This European European Standard Standard EN EN 1993, 1993, Eurocode Eurocode 3: 3: Design Design of of steel steel structures, structures, has has been been prepared prepared by by Technical Technical Committee CEN/TC250 « Structural Eurocodes », the Secretariat of which is held by BSI CEN/TC250 Committee CEN/TC250 « Structural Eurocodes », the Secretariat of which is held by BSI CEN/TC250 is is responsible responsible for for all all Structural Structural Eurocodes Eurocodes This This European European Standard Standard shall shall be be given given the the status status of of aa National National Standard, Standard, either either by by publication publication of of an an identical identical text or by endorsement, at the latest by November 2005, and conflicting National Standards shall be text or by endorsement, at the latest by November 2005, and conflicting National Standards shall be withdrawn withdrawn at at latest latest by by March March 2010 2010 This This Eurocode Eurocode supersedes supersedes ENV ENV 1993-1-1 1993-1-1 According According to to the the CEN-CENELEC CEN-CENELEC Internal Internal Regulations, Regulations, the the National National Standard Standard Organizations Organizations of of the the EN 1993-1-1:2005/A1:2014 (E) following countries are bound to implement these European Standard: Austria, Belgium, Cyprus, Czech following countries are bound to implement these European Standard: Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Slovenia, Spain, Lithuania, Luxembourg, Luxembourg, Malta, Malta, Netherlands, Netherlands, Norway, Norway, Poland, Poland, Portugal, Portugal, Slovakia, Slovakia,BS Slovenia, Spain, Sweden, Sweden, EN 1993-1-1:2005 Switzerland and United Kingdom Switzerland and United Kingdom EN 1993-1-1:2005 (E) Background of Foreword Foreword to amendment A1 programme Background of the the Eurocode Eurocode programme In 1975, the the on an action programme field of This European Standard ENof EurocodeCommunity 3:has Design steel structures, has been preparedin Technical This document (EN 1993-1-1:2005/A1:2014) beenofdecided prepared Committee CEN/TC In 1975, the Commission Commission of1993, the European European Community decided onby an Technical action programme inbythe the field 250 of construction, based on article 95 of the Treaty The objective of the programme was the elimination of Committee CEN/TC250 « Structural Eurocodes », the Secretariat of which is held by BSI CEN/TC250 is “Structural Eurocodes”, secretariat of which is held BSI construction, based on the article 95 of the Treaty The by objective of the programme was the elimination of technical obstacles to the responsible for all Structural Eurocodes technical obstacles to trade trade and and the harmonization harmonization of of technical technical specifications specifications This Amendment to the European Standard EN 1993-1-1:2005 shall be given the status of a national This European Standard shall bethe given statustook of National Standard, either byset of an2015, identical Within this action programme, Commission initiative to of technical standard, by publication of an the identical texta the or by endorsement, at aathe latest by May and Within thiseither action programme, the Commission took the initiative to establish establish setpublication of harmonized harmonized technical conflicting national the latest by May 2015 text orforbythe endorsement, at theshall latestbe bywithdrawn November and conflicting National shall be withdrawn rules designstandards of construction works which,atin2005, a first stage, would serve as anStandards alternative to the national rules for the design of construction works which, in a first stage, would serve as an alternative to the national at latest by March rules in in Member rules in force force in the the2010 Member States States and, and, ultimately, ultimately, would would replace replace them them Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights CENyears, [and/or CENELEC] not be for Committee identifying any all such patent rights Thisfifteen Eurocode supersedes ENVshall 1993-1-1 theheld helpresponsible of a Steering withorRepresentatives of Member For the Commission, with For fifteen years, the Commission, with the help of a Steering Committee with Representatives of Member States, conducted conducted the the development development of of the the Eurocodes Eurocodes programme, programme, which which led led to to the the first first generation generation of of States, According totothe CEN-CENELEC Internal Regulations, the national standards organizations of the following According the CEN-CENELEC Internal Regulations, the National Standard Organizations of the European codes in the 1980s European are codes in the 1980s countries bound to Europeanthese Standard: Austria, Belgium, Bulgaria, Croatia,Cyprus, Cyprus,Czech Czech following countries areimplement bound tothis implement European Standard: Austria, Belgium, Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Republic, Denmark, Estonia, Finland, France, Hungary, Ireland, Italy, Latvia,11 In 1989, the the Commission and the the Member StatesGermany, of the the EU EU Greece, and EFTA EFTA decided,Iceland, on the the basis basis of an an agreement In 1989, Commission Member States of and decided, on agreement Hungary, Iceland, Ireland,and Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,of Poland, Portugal, Lithuania,the Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, between Commission and CEN, to the and the publication of to between the Commission andSpain, CEN, to transfer transfer the preparation preparation and thethe publication of the the Eurocodes Eurocodes to the the Romania, Slovakia, Slovenia, Sweden, Switzerland, Turkey and United Kingdom Switzerland and United Kingdom CEN through a series of Mandates, in order to provide them with a future status of European Standard CEN through a series of Mandates, in order to provide them with a future status of European Standard (EN) (EN) This This links links de de facto facto the the Eurocodes Eurocodes with with the the provisions provisions of of all all the the Council’s Council’s Directives Directives and/or and/or Commission’s Commission’s Decisions dealing with European standards (e.g the Council Directive 89/106/EEC on Background theEuropean Eurocode programme Decisions dealingof with standards (e.g the Council Directive 89/106/EEC on construction construction products products – – CPD CPD –– and and Council Council Directives Directives 93/37/EEC, 93/37/EEC, 92/50/EEC 92/50/EEC and and 89/440/EEC 89/440/EEC on on public public works works and and services services and and equivalent EFTA Directives in of the In 1975, the Commission the European Community decided on anmarket) action programme in the field of equivalent EFTA Directivesofinitiated initiated in pursuit pursuit of setting setting up up the internal internal market) construction, based on article 95 of the Treaty The objective of the programme was the elimination of The Eurocode programme comprises standards technical obstacles to trade and the harmonization offollowing technical specifications The Structural Structural Eurocode programme comprises the the following standards generally generally consisting consisting of of aa number number of of Parts: Parts: Within thisEurocode: action programme, thestructural Commission took the initiative to establish a set of harmonized technical EN Basis design EN 1990 1990 Basis of of structural design rules for theEurocode: design of construction works which, in a first stage, would serve as an alternative to the national EN Eurocode 1: structures rules in force in the Member Stateson ultimately, would replace them Eurocode 1: Actions Actions onand, structures EN 1991 1991 EN EN 1992 1992 Eurocode Eurocode 2: 2: Design Design of of concrete concrete structures structures For fifteen years, the Commission, with the help of a Steering Committee with Representatives of Member EN 1993 Eurocode 3: Design of steel structures EN 1993conducted Eurocode Design of steel structures States, the3: development of the Eurocodes programme, which led to the first generation of EN 1994 Eurocode 4: Design of composite European codes in the 1980s EN 1994 Eurocode 4: Design of composite steel steel and and concrete concrete structures structures EN 1995 Eurocode 5: Design of timber structures EN1989, 1995theEurocode 5: Design timber States structures In Commission and the of Member of the EU and EFTA decided, on the basis of an agreement1 EN 1996 Eurocode 6: Design of masonry structures between Commission and CEN, to transfer the preparation and the publication of the Eurocodes to the EN 1996 theEurocode 6: Design of masonry structures CEN through a series of Mandates, in order to provide them with a future status of European Standard (EN) EN EN 1997 1997 Eurocode Eurocode 7: 7: Geotechnical Geotechnical design design This links de facto the Eurocodes with the provisions of all the Council’s Directives and/or Commission’s EN 1998 Eurocode 8: Design structures for earthquake resistance EN 1998 dealing Eurocode 8: European Design of of structures forthe earthquake Decisions with standards (e.g Council resistance Directive 89/106/EEC on construction products – CPD – and Council Directives 93/37/EEC, 92/50/EEC and 89/440/EEC on public works and services and equivalent EFTA Directives initiated in pursuit of setting up the internal market) Agreement between the Commission of the European Communities and the European Committee for Standardisation (CEN) Agreement between the Commission of the European Communities and the European Committee for Standardisation (CEN) concerning the work on EUROCODES for the design of building and civil engineering works (BC/CEN/03/89) concerning the work on EUROCODES for the design of building and civil engineering works (BC/CEN/03/89) The Structural Eurocode programme comprises the following standards generally consisting of a number of Parts: 5 EN 1990 Eurocode: Basis of structural design In 1989, the Commission and the Member States of the EU and EFTA decided, on the basis of an agreement1 BS EN 1993-1-1:2005+A1:2014 between the Commission and CEN, BS EN 1993-1-1:2005 EN 1993-1-1:2005+A1:2014 (E) to transfer the preparation and the publication of the Eurocodes to the CEN through a series of Mandates, in order to provide them with a future status of European Standard (EN) EN 1993-1-1:2005 (E) This links de facto the Eurocodes with the provisions of all the Council’s Directives and/or Commission’s EN 1999 Eurocode 9: Design of aluminium structures Decisions dealing with European standards (e.g the Council Directive 89/106/EEC on construction products – CPD – and Council Directives 93/37/EEC, 92/50/EEC and 89/440/EEC on public works and services and Eurocode standards recognize the responsibility of regulatory authorities in each Member State and have equivalent EFTA Directives initiated in pursuit of setting up the internal market) safeguarded their right to determine values related to regulatory safety matters at national level where these continue to vary from State to State The Structural Eurocode programme comprises the following standards generally consisting of a number of Parts: Status and field of application of Eurocodes EN 1990 Eurocode: Basis of structural design The Member States of EU and recognize that Eurocodes serve as reference documents for the EN 1991 Eurocode 1: the Actions on EFTA structures following purposes : EN 1992 Eurocode 2: Design of concrete structures – as a means to prove compliance of building and civil engineering works with the essential requirements EN 1993 Eurocode 3: Design of steelparticularly structures Essential Requirement N°1 - Mechanical resistance and of Council Directive 89/106/EEC, EN 1994 4: Design of composite andinconcrete structures stabilityEurocode - and Essential Requirement N°2 -steel Safety case of fire; EN 1995 Eurocode 5: Design of timber structures works and related engineering services; – as a basis for specifying contracts for construction EN 1996 Eurocodefor 6: drawing Design up of masonry structures – as a framework harmonized technical specifications for construction products (ENs and ETAs) Eurocode 7: Geotechnical design EN 1997 BS EN 1993-1-1:2005 EN Eurocode Design of structures for earthquake The1998 Eurocodes, as far8:as they concern the construction worksresistance themselves, have a direct relationship with the EN 1993-1-1:2005 (E) referred to in Articlestructures 12 of the CPD, although they are of a different nature from Interpretative Documents EN 1999 Eurocode 9: Design of aluminium harmonized product standard Therefore, technical aspects arising from the Eurocodes work need to be Agreement between the Commission of the European Communities and the European Committee for Standardisation (CEN) adequately considered by CEN Technical Committees and/or EOTA Working Groups working product Eurocode thefor responsibility of regulatory authorities in each Member Stateonand have concerningstandards the work onrecognize EUROCODES the design of building and civil engineering works (BC/CEN/03/89) standards with a view compatibility of these technical specifications withlevel the Eurocodes safeguarded their righttotoachieving determinea full values related to regulatory safety matters at national where these continue to vary from State to State The Eurocode standards provide common structural design rules for everyday use for the design of whole a traditional and an innovative nature Unusual forms of structuresand and field component products of of both Status of application Eurocodes construction or design conditions are not specifically covered and additional expert consideration will be required by theStates designer in such cases The Member of the EU and EFTA recognize that Eurocodes serve as reference documents for the following purposes : National Standards implementing Eurocodes as a means to prove compliance of building and civil engineering works with the essential requirements of CouncilStandards Directiveimplementing 89/106/EEC, Eurocodes particularlywill Essential Requirement - Mechanical resistance and The National comprise the full textN°1 of the Eurocode (including any stability and Essential Requirement N°2 Safety in case of fire; annexes), as published by CEN, which may be preceded by a National title page and National foreword, and – –mayas basis for by specifying contracts for construction bea followed a National annex (informative) works and related engineering services; as a framework for drawing up harmonized technical specifications for construction products (ENs and The ETAs) National Annex (informative) may only contain information on those parameters which are left open in the Eurocode for national choice, known as Nationally Determined Parameters, to be used for the design of buildings and civil engineering works to constructed works in the country concerned, : relationship with the The Eurocodes, as far as they concern thebeconstruction themselves, have a i.e direct – referred to in Article of the CPD, are of a different nature from Interpretative – values for Documents partial factors and/or classes where12 alternatives arealthough given in they the Eurocode, Therefore, technical aspects arising from the Eurocodes work need to be harmonized product standard – values to be used where a symbol only is given in the Eurocode, adequately considered by CEN Technical Committees and/or EOTA Working Groups working on product – geographical and climatic data aspecific to the Member State, e.g snow map, standards with a view to achieving full compatibility of these technical specifications with the Eurocodes – the procedure to be used where alternative procedures are given in the Eurocode, The Eurocode standards provide common structural design rules for everyday use for the design of whole – references non-contradictory information assist the user to apply Unusual the Eurocode forms of structures and tocomponent productscomplementary of both a traditional andtoan innovative nature construction or design conditions are not specifically covered and additional expert consideration will be Links between Eurocodes and product harmonized technical specifications (ENs required by the designer in such cases National implementing Eurocodes According toStandards Art 3.3 of the CPD, the essential requirements (ERs) shall be given concrete form in interpretative documents for the creation of the necessary links between the essential requirements and the mandates for hENs and ETAGs/ETAs The National Standards implementing Eurocodes will comprise the full text of the Eurocode (including any Accordingas to published Art 12 of theby CPD the interpretative shall :by a National title page and National foreword, and annexes), CEN, which maydocuments be preceded a) give concrete form to the essential requirements by harmonizing the terminology and the technical bases and indicating classes may be followed by a National annex (informative) or levels for each requirement where necessary ; b) indicate methods of correlating these classes or levels of requirement with the technical specifications, e.g methods of The National (informative) may information on those parameters which are left open in calculation Annex and of proof, technical rules for only projectcontain design, etc ; serve as a reference for thechoice, establishment of harmonized standards and guidelines for European thec) Eurocode for national known as Nationally Determined Parameters, totechnical be usedapprovals for the design of The Eurocodes, de facto, play a similar role in the field of the ER and a part of ER buildings and civil engineering works to be constructed in the country concerned, i.e : – values for partial factors and/or classes where alternatives are given in the Eurocode, – values to be used where a symbol only is given in the Eurocode, – geographical and climatic data specific to the Member State, e.g snow map, The Eurocode standards provide common structural design rules for everyday use for the design of whole structures and component products of both a traditional and an innovative nature Unusual forms of BS EN 1993-1-1:2005+A1:2014 BS EN 1993-1-1:2005 construction or design conditions are not specifically covered and additional expert consideration will be EN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) required by the designer in such cases and ETAs) National Standards implementing Eurocodes There is a need for consistency between the harmonized technical specifications for construction products The the National Standards implementing Eurocodes all willthe comprise the full text of the Eurocode (including and technical rules for works4 Furthermore, information accompanying the CE Marking of any the annexes), as published CEN,refer which be preceded by clearly a National title page and Nationally National foreword, and construction products by which to may Eurocodes should mention which Determined may be followed by a National (informative) Parameters have been taken intoannex account The National Annex (informative) may only information on those parameters which are left open in Additional information specific to contain EN 1993-1 the Eurocode for national choice, known as Nationally Determined Parameters, to be used for the design of buildings and civil engineering to be constructed country concerned, i.e : EN 1991 – Actions on EN 1993 is intended to be used works with Eurocodes EN 1990in–the Basis of Structural Design, structures and EN 1992 to EN 1999, when steel structures or steel components are referred to – values for partial factors and/or classes where alternatives are given in the Eurocode, given in the Eurocode, EN values 1993-1toisbetheused firstwhere of sixa symbol parts ofonly EN is 1993 – Design of Steel Structures It gives generic design rules to be used with thedata other parts toEN EN 1993-6 also gives supplementary rules –intended geographical and climatic specific the1993-2 MembertoState, e.g snowItmap, applicable only to buildings – the procedure to be used where alternative procedures are given in the Eurocode, – –EN references to non-contradictory complementary information assist the user apply the Eurocode 1993-1 comprises twelve subparts EN 1993-1-1 to EN to1993-1-12 eachtoaddressing specific steel components, limit states or materials BS EN 1993-1-1:2005 Links between Eurocodes and product harmonized technicalEN specifications (ENs 1993-1-1:2005 (E) It may also be used for design cases not covered by the Eurocodes (other structures, other actions, other and ETAs) materials) serving as a reference document for other CEN TC´s concerning structural matters According to Art 3.3 of the CPD, the essential requirements (ERs) shall be given concrete form in interpretative documents for the There is of a the need for consistency therequirements harmonized specifications for construction products creation necessary links betweenbetween the essential andtechnical the mandates for hENs and ETAGs/ETAs EN 1993-1 is intended for use by and the technical rules for works Furthermore, all the information accompanying the CE Marking of the to Art 12 of thewhich CPD therefer interpretative documents shall : execution – According committees drafting design related testing and standards, construction products to product, Eurocodes should clearly mention which Nationally Determined a) give concrete form to the essential requirements by harmonizing the terminology and the technical bases and indicating classes Parameters have been taken into account or levels(e.g for each where necessary ; – clients for requirement the formulation of their specific requirements) b) indicate methods of correlating these classes or levels of requirement with the technical specifications, e.g methods of – designers constructors calculation and and of proof, technical rules for project design, etc ; Additional information specific to EN 1993-1 – c) serve as a reference for the establishment of harmonized standards and guidelines for European technical approvals relevant authorities The Eurocodes, de facto, play a similar role in the field of the ER and a part of ER EN 1993 is intended to be used with Eurocodes EN 1990 – Basis of Structural Design, EN 1991 – Actions on structures and EN 1992 to ENfactors 1999, when steel reliability structures or steel components are referred Numerical values for partial and other parameters are recommended asto basic values that provide an acceptable level of reliability They have been selected assuming that an appropriate level of EN 1993-1 is the first of six parts of EN 1993 – Design of Steel Structures It gives generic design rules workmanship and quality management applies intended to be used with the other parts EN 1993-2 to EN 1993-6 It also gives supplementary rules applicable only to buildings EN 1993-1 comprises twelve subparts EN 1993-1-1 to EN 1993-1-12 each addressing specific steel components, limit states or materials It may also be used for design cases not covered by the Eurocodes (other structures, other actions, other materials) serving as a reference document for other CEN TC´s concerning structural matters EN 1993-1 is intended for use by – committees drafting design related product, testing and execution standards, – clients (e.g for the formulation of their specific requirements) – designers and constructors – relevant authorities Numerical values for partial factors and other reliability parameters are recommended as basic values that provide an acceptable level of reliability They have been selected assuming that an appropriate level of workmanship and quality management applies See Art.3.3 and Art.12 of the CPD, as well as clauses 4.2, 4.3.1, 4.3.2 and 5.2 of ID 7 BS EN 1993-1-1:2005+A1:2014 BS EN 1993-1-1:2005 EN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) Annex B [informative] – Method 2: Interaction factors kij for interaction formula in 6.3.3(4) Table B.1: Interaction factors kij for members not susceptible to torsional deformations Interaction factors Type of sections I-sections RHS-sections kyy I-sections RHS-sections I-sections RHS-sections kyz kzy I-sections kzz RHS-sections Design assumptions elastic cross-sectional properties plastic cross-sectional properties class 3, class class 1, class N Ed C my 1 + 0,6λ y N / χ γ y Rk M N Ed ≤ C my 1 + 0,6 N / χ γ y Rk M1 N Ed C my 1 + λ y − 0,2 N / χ γ y Rk M N Ed ≤ C my 1 + 0,8 N / χ γ y Rk M1 kzz 0,6 kzz 0,8 kyy 0,6 kyy N Ed C mz 1 + 0,6λ z N / χ γ z Rk M1 N Ed ≤ C mz 1 + 0,6 χ z N Rk / γ M1 ( ) ( ) ( ) N Ed C mz 1 + 2λ z − 0,6 χ z N Rk / γ M1 N Ed ≤ C mz 1 + 1,4 N / χ γ z Rk M1 N Ed C mz 1 + λ z − 0,2 N / χ γ z Rk M N Ed ≤ C mz 1 + 0,8 χ z N Rk / γ M1 For I- and H-sections and rectangular hollow sections under axial compression and uniaxial bending My,Ed the coefficient kzy may be kzy = Table B.2: Interaction factors kij for members susceptible to torsional deformations Interaction factors kyy kyz kzy Design assumptions elastic cross-sectional properties plastic cross-sectional properties class 3, class class 1, class kyy from Table B.1 kyy from Table B.1 kyz from Table B.1 kyz from Table B.1 N Ed 0,05λ z 1 − (C mLT − 0,25) χ z N Rk / γ M1 N Ed 0,05 ≥ 1 − (C mLT − 0,25) χ z N Rk / γ M1 N Ed 0,1λ z 1 − (C mLT − 0,25) χ z N Rk / γ M1 N Ed 0,1 ≥ 1 − (C mLT − 0,25) χ z N Rk / γ M1 for λ z < 0,4 : k zy = 0,6 + λ z ≤ − N Ed 0,1λ z (C mLT − 0,25) χ z N Rk / γ M1 79 79 BS EN 1993-1-1:2005+A1:2014 BS 1993-1-1:2005 ENEN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) kzz kzz from Table B.1 kzz from Table B.1 Table B.3: Equivalent uniform moment factors Cm in Tables B.1 and B.2 Moment diagram range Cmy and Cmz and CmLT uniform loading concentrated load -1 ≤ ψ ≤ 0,6 + 0,4ψ ≥ 0,4 ≤ αs ≤ -1 ≤ αs < 0 ≤ αh ≤ -1 ≤ αh < -1 ≤ ψ ≤ 0,2 + 0,8αs ≥ 0,4 0,2 + 0,8αs ≥ 0,4 0≤ψ≤1 0,1 - 0,8αs ≥ 0,4 -0,8αs ≥ 0,4 -1 ≤ ψ < 0,1(1-ψ) - 0,8αs ≥ 0,4 0,2(-ψ) - 0,8αs ≥ 0,4 -1 ≤ ψ ≤ 0,95 + 0,05αh 0,90 + 0,10αh 0≤ψ≤1 0,95 + 0,05αh 0,90 + 0,10αh -1 ≤ ψ < 0,95 + 0,05αh(1+2ψ) Š0,90 + 0,10αh(1+2ψ)‹ For members with sway buckling mode the equivalent uniform moment factor should be taken Cmy = 0,9 or ŠCmz‹ = 0,9 respectively Cmy , Cmz and CmLT should be obtained according to the bending moment diagram between the relevant braced points as follows: moment factor Cmy Cmz CmLT 80 80 bending axis y-y z-z y-y points braced in direction z-z y-y y-y BS EN 1993-1-1:2005+A1:2014 EN1993-1-1:2005+A1:2014 1993-1-1:2005/A1:2014 (E) (E) EN Annex C (normative) Selection of execution class C.1 General C.1.1 Basic requirements (1)P To obtain the reliability of the completed works required according to EN 1990 an appropriate execution class shall be selected This annex forms the basis for this selection C.1.2 Execution class (1) Execution class (EXC) is defined as a classified set of requirements specified for the execution of the works as a whole, of an individual component or of a detail of a component (2) In order to specify requirements for the execution of steel structures to EN 1090-1 and EN 1090-2 the choice of execution class, EXC1, EXC2, EXC3 or EXC4, should be made prior to the commencement of execution The execution requirements are progressively more onerous from EXC1 up to EXC4 NOTE EN 1993 and EN 1994 are based on the assumption that they are used in conjunction with EN 1090-1 and EN 1090-2 EN 1993-1-9, EN 1993-2, EN 1993-3-1 and EN 1993-3-2 give supplementary requirements to EN 1090-2 for the execution of structures or components or details subject to fatigue actions In addition to EN 1090-2, EN 1993-5 refers to other European Standards for the execution of piling works NOTE EN 1090-2 states that EXC2 should apply if no execution class is specified C.2 Selection process C.2.1 Governing factors (1) The selection of the execution class should be based on the following three factors: − the required reliability; − the type of structure, component or detail; and − the type of loading for which the structure, component or detail is designed C.2.2 Selection (1) In terms of reliability management, the selection of execution class should be based on either the required consequences class (CC) or the reliability class (RC) or both The concepts of reliability class and consequences class are defined in EN 1990 (2) In terms of the type of loading applied to a steel structure or component or detail, the selection of execution class should be based on whether the structure or component or detail is designed for static actions, quasi-static actions, fatigue actions or seismic actions (3) The selection of execution class (EXC) should be based on Table C.1. 81 BS EN 1993-1-1:2005+A1:2014 EN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005/A1:2014 (E) Table C.1 ― Choice of execution class (EXC) Reliability Class (RC) or Consequences Class (CC) Static, quasi-static or a seismic DCL RC3 or CC3 EXC3 EXC3c RC2 or CC2 EXC2 EXC3 RC1 or CC1 EXC1 EXC2 a b c Type of loading b Fatigue or a seismic DCM or DCH c Seismic ductility classes are defined in EN 1998-1: Low = DCL; Medium = DCM; High = DCH See EN 1993-1-9 EXC4 may be specified for structures with extreme consequences of structural failure NOTE The National Annex may specify whether the selection of execution classes is based on reliability classes or consequences classes or both and may specify the choice in terms of the type of the structure The National Annex may specify whether Table C.1 is to be adopted NOTE Designs to EN 1993-4-1 and EN 1993-4-2 depend on the choice of consequences class Designs to EN 19933-1 and EN 1993-3-2 depend on the choice of reliability class (4) If the required execution class for particular components and/or details is different from that applicable to the structure in general, then these components and/or details should be clearly identified NOTE The National Annex may specify the choice of execution class in terms of types of components or details The following is recommended: If EXC1 is selected for a structure, then EXC2 should apply to the following types of component: a) welded components manufactured from steel products of grade S355 and above; b) welded components essential for structural integrity that are assembled by welding on the construction site; c) welded components of CHS lattice girders requiring end profile cuts; d) components with hot forming during manufacturing or receiving thermic treatment during manufacturing (5) Specification of a higher execution class for the execution of a structure or component or detail should not be used to justify the use of lower partial factors for resistance in the design of that structure or component or detail. " 82 BS EN 1993-1-1:2005+A1:2014 BS EN 1993-1-1:2005 EN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) Annex AB [informative] – Additional design provisions AB.1 Structural analysis taking account of material non-linearities (1)B In case of material non-linearities the action effects in a structure may be determined by incremental approach to the design loads to be considered for the relevant design situation (2)B In this incremental approach each permanent or variable action should be increased proportionally AB.2 Simplified provisions for the design of continuous floor beams (1)B For continuous beams with slabs in buildings without cantilevers on which uniformly distributed loads are dominant, it is sufficient to consider only the following load arrangements: a) alternative spans carrying the design permanent and variable load (γG Gk + γQ Qk), other spans carrying only the design permanent load γG Gk b) any two adjacent spans carrying the design permanent and variable loads (γG Gk + γQ Qk), all other spans carrying only the design permanent load γG Gk NOTE a) applies to sagging moments, b) to hogging moments NOTE This annex is intended to be transferred to EN 1990 in a later stage 81 83 BS EN 1993-1-1:2005+A1:2014 BS 1993-1-1:2005 ENEN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) Annex BB [informative] – Buckling of components of building structures BB.1 Flexural buckling of members in triangulated and lattice structures BB.1.1 General (1)B For chord members generally and for out-of-plane buckling of web members, the buckling length Lcr may be taken as equal to the system length L, see BB.1.3(1)B, unless a smaller value can be justified by analysis (2)B The buckling length Lcr of an I or H section chord member may be taken as 0,9L for in-plane buckling and 1,0L for out-of-plane buckling, unless a smaller value is justified by analysis (3)B Web members may be designed for in-plane buckling using a buckling length smaller than the system length, provided the chords supply appropriate end restraint and the end connections supply appropriate fixity (at least bolts if bolted) (4)B Under these conditions, in normal triangulated structures the buckling length Lcr of web members for in-plane buckling may be taken as 0,9L, except for angle sections, see BB.1.2 BB.1.2 Angles as web members (1)B Provided that the chords supply appropriate end restraint to web members made of angles and the end connections of such web members supply appropriate fixity (at least two bolts if bolted), the eccentricities may be neglected and end fixities allowed for in the design of angles as web members in compression The effective slenderness ratioλeff may be obtained as follows: λ eff , v = 0,35 + 0,7λ v for buckling about v-v axis λ eff , y = 0,50 + 0,7λ y for buckling about y-y axis λ eff ,z = 0,50 + 0,7λ z for buckling about z-z axis (BB.1) whereλ is as defined in 6.3.1.2 (2)B When only one bolt is used for end connections of angle web members the eccentricity should be taken into account using 6.2.9 and the buckling length Lcr should be taken as equal to the system length L BB.1.3 Hollow sections as members (1)B The buckling length Lcr of a hollow section chord member may be taken as 0,9L for both in-plane and out-of-plane buckling, where L is the system length for the relevant plane The in-plane system length is the distance between the joints The out-of-plane system length is the distance between the lateral supports, unless a smaller value is justified by analysis (2)B The buckling length Lcr of a hollow section brace member (web member) with bolted connections may be taken as 1,0L for both in-plane and out-of-plane buckling Š (3)B The buckling length Lcr of a hollow section brace member without cropping or flattening, welded around its perimeter to hollow section chords, may be generally taken as 0,75L for both in-plane and outof-plane buckling Lower buckling lengths may be used based on testing or calculations In this case the buckling length of the cord may not be reduced.‹ NOTE The National Annex may give more information on buckling lengths 82 84 BS EN 1993-1-1:2005+A1:2014 BS EN 1993-1-1:2005 EN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) BB.2 Continuous restraints BB.2.1 Continuous lateral restraints (1)B If trapezoidal sheeting according to EN 1993-1-3 is connected to a beam and the condition expressed Š by formula (BB.2)‹ is met, the beam at the connection may be regarded as being laterally restrained in the plane of the sheeting Š S ≥ EI w where S Iw 70 π2 π2 + GI + EI 0,25h ‹ T z 2 L L h (BB.2) is the shear stiffness (per unit of beam length) provided by the sheeting to the beam regarding its deformation in the plane of the sheeting Što be connected to the beam at the bottom at each rib‹ is the warping constant ŠIT ‹ is the torsion constant Iz is the second moment of area of the cross section about the minor axis of the cross section L is the beam length h is the depth of the beam If the sheeting is connected to a beam at every second rib only, S should be substituted by 0,20S NOTE ŠFormula (BB.2)‹ may also be used to determine the lateral stability of beam flanges used in combination with other types of cladding than trapezoidal sheeting, provided that the connections are of suitable design BB.2.2 Continuous torsional restraints (1)B A beam may be considered as sufficiently restraint from torsional deformations if C ϑ, k > M 2pl,k EI z K ϑK υ (BB.3) where Cϑ,k = rotational stiffness (per unit of beam length) provided to the beam by the stabilizing continuum (e.g roof structure) and the connections Kυ = 0,35 for elastic analysis Kυ = 1,00 for plastic analysis Kϑ = factor for considering the moment distribution see Table BB.1 and the type of restraint Mpl,k = characteristic value of the plastic moment of the beam 83 85 BS EN 1993-1-1:2005+A1:2014 BS 1993-1-1:2005 ENEN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) Table BB.1: Factor Kϑ for considering the moment distribution and the type of restraint Case M 4,0 M 2a 2b without with translational translational restraint restraint Moment distribution M 0,12 3,5 M M 0,23 M M M 2,8 1,6 1,0 1,0 0,7 (2)B The rotational stiffness provided by the stabilizing continuum to the beam may be calculated from 1 1 = + + C ϑ,k C ϑR ,k C ϑC,k C ϑD ,k (BB.4) where CϑR,k = rotational stiffness (per unit of the beam length) provided by the stabilizing continuum to the beam assuming a stiff connection to the member CϑC,k = rotational stiffness (per unit of the beam length) of the connection between the beam and the stabilizing continuum CϑD,k = rotational stiffness (per unit of the beam length) deduced from an analysis of the distorsional deformations of the beam cross sections, where the flange in compression is the free one; where the compression flange is the connected one or where distorsional deformations of the cross sections may be neglected (e.g for usual rolled profiles) CϑD,k = ∞ NOTE For more information see EN 1993-1-3 BB.3 Stable lengths of segment containing plastic hinges for out-of-plane buckling BB.3.1 Uniform members made of rolled sections or equivalent welded I-sections BB.3.1.1 Stable lengths between adjacent lateral restraints (1)B Lateral torsional buckling effects may be ignored where the length L of the segment of a member between the restrained section at a plastic hinge location and the adjacent lateral restraint is not greater than Lm, where: 84 86 BS EN 1993-1-1:2005+A1:2014 BS EN 1993-1-1:2005 EN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) ŠLm = where NEd A 38i z N Ed + 57,4 A 756 C12 W AIT pl , y f y 235 (BB.5) ‹ is the design value of the compression force [N] in the member is the cross section area [mm²] of the member Wpl,y is the plastic section modulus of the member Š IT‹ is the torsion constant of the member fy ŠC1 is the yield strength in [N/mm²] is a factor depending on the loading and end conditions and may be taken as C1 = kc−2 where kc is to be taken from Table 6.6.‹ provided that the member is restrained at the hinge as required by 6.3.5 and that the other end of the segment is restrained – either by a lateral restraint to the compression flange where one flange is in compression throughout the length of the segment, – or by a torsional restraint, – or by a lateral restraint at the end of the segment and a torsional restraint to the member at a distance that satisfies the requirements for Ls, see Figure BB.1, Figure BB.2 and Figure BB3 NOTE In general Ls is greater than Lm tension flange plastic stable length (see BB.3.1.1) elastic section (see 6.3) plastic hinge restraints bending moment diagram compression flange plastic with tension flange restraint, stable length = Ls (see BB.3.1.2, equation (BB.7) or (BB.8)) elastic with tension flange restraint (see 6.3), χ and χLT from Ncr and Mcr including tension flange restraint Figure BB.1: Checks in a member without a haunch 85 87 BS EN 1993-1-1:2005+A1:2014 BS 1993-1-1:2005 ENEN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) tension flange elastic section (see 6.3) plastic stable length (see BB.3.2.1) or elastic (see 6.3.5.3(2)B) plastic stable length (see BB.3.1.1) elastic section (see 6.3) plastic hinge restraints bending moment diagram compression flange 10 plastic stable length (see BB.3.2) or elastic (see 6.3.5.3(2)B) 11 plastic stable length (see BB.3.1.2) 12 elastic section (see 6.3), χ and χLT from Ncr and Mcr including tension flange restraint Figure BB.2: Checks in a member with a three flange haunch tension flange elastic section (see 6.3) plastic stable length (see BB.3.2.1) plastic stable length (see BB.3.1.1) elastic section (see 6.3) plastic hinge restraints bending moment diagram compression flange 10 plastic stable length (see BB.3.2) 11 plastic stable length (see BB.3.1.2) 12 elastic section (see 6.3), χ and χLT from Ncr and Mcr including tension flange restraint Figure BB.3: Checks in a member with a two flange haunch 86 88 BS EN 1993-1-1:2005+A1:2014 BS EN 1993-1-1:2005 EN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) BB.3.1.2 Stable length between torsional restraints (1)B Lateral torsional buckling effects may be ignored where the length L of the segment of a member between the restrained section at a plastic hinge location and the adjacent torsional restraint subject to a constant moment is not greater than Lk, provided that – the member is restrained at the hinge as required by 6.3.5 and – there are one or more intermediate lateral restraints between the torsional restraints at a spacing that satisfies the requirements for Lm, see BB.3.1.1, where 600f y h i z 5,4 + E t f Lk = f y h 5,4 − E t f (BB.6) (2)B Lateral torsional buckling effects may be ignored where the length L of the segment of a member between the restrained section at a plastic hinge location and the adjacent torsional restraint subject to a linear moment gradient and axial compression is not greater than Ls, provided that – the member is restrained at the hinge as required by 6.3.5 and – there are one or more intermediate lateral restraints between the torsional restraints at a spacing that satisfies the requirements for Lm, see BB.3.1.1, where L s = M pl, y ,Rk Cm Lk M N , y ,Rk + aN Ed (BB.7) Cm is the modification factor for linear moment gradient, see BB.3.3.1; a is the distance between the centroid of the member with the plastic hinge and the centroid of the restraint members; Mpl,y,Rk is the characteristic plastic moment resistance of the cross section about the y-y axis MN,y,Rk is the characteristic plastic moment resistance of the cross section about the y-y axis with reduction due to the axial force NEd (3)B Lateral torsional buckling effects may be ignored where the length L of a segment of a member between the restrained section at a plastic hinge location and the adjacent torsional restraint subject to a non linear moment gradient and axial compression is not greater than Ls, provided that – the member is restrained at the hinge as required by 6.3.5 and – there are one or more intermediate lateral restraints between the torsional restraints at a spacing that satisfies the requirements for Lm, Šsee BB.3.1.1‹ where L s = Cn Lk (BB.8) Cn is the modification factor for non-linear moment gradient, see BB.3.3.2, see Figure BB.1, Figure BB.2 and Figure BB.3 87 89 BS EN 1993-1-1:2005+A1:2014 BS 1993-1-1:2005 ENEN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) BB.3.2 Haunched or tapered members made of rolled sections or equivalent welded Isections BB.3.2.1 Stable length between adjacent lateral restraints (1)B Lateral torsional buckling effects may be ignored where the length L of the segment of a member between the restrained section at a plastic hinge location and the adjacent lateral restraint is not greater than Lm, where for three flange haunches (see Figure BB.2) – Š Lm = 38i z N Ed + 57,4 A 756 C12 W AI T pl , y f y 235 (BB.9) ‹ for two flange haunches (see Figure BB.3) – ŠL m = 0,85 where NEd Š Wpl2 , y AI T A Š C1 Wpl,y 38i z N Ed Wpl, y f y + 57,4 A 756 C12 AI T 235 (BB.10) ‹ is the design value of the compression force [N] in the member ‹ is the maximum value in the segment is the cross sectional area [mm²] at the location where Š Wpl2 , y AI T ‹ is a maximum of the tapered member is a factor depending on the loading and end conditions and may be taken as C1 = kc−2 where kc is to be taken from Table 6.6.‹ is the plastic section modulus of the member Š I T ‹ is the torsional constant of the member fy is the yield strength in [N/mm²] is the minimum value of the radius of gyration in the segment iz provided that the member is restrained at the hinge as required by 6.3.5 and that the other end of segment is restrained – either by a lateral restraint to the compression flange where one flange is in compression throughout the length of the segment, – or by a torsional restraint, – or by a lateral restraint at the end of the segment and a torsional restraint to the member at a distance that satisfies the requirements for Ls BB.3.2.2 Stable length between torsional restraints (1)B For non uniform members with constant flanges under linear or non-linear moment gradient and axial compression, lateral torsional buckling effects may be ignored where the length L of the segment of a member between the restrained section at a plastic hinge location and the adjacent torsional restraint is not greater than Ls, provided that – the member is restrained at the hinge as required by 6.3.5 and – there are one or more intermediate lateral restraints between the torsional restraints at a spacing that satisfies the requirements for Lm, see BB.3.2.1, 88 90 BS EN 1993-1-1:2005+A1:2014 BS EN 1993-1-1:2005 EN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) where – for three flange haunches (see Figure BB.2) Cn Lk Ls = – (BB.11) c for two flange haunches (see Figure BB.3) L s = 0,85 Cn Lk (BB.12) c where Lk is the length derived for a uniform member with a cross-section equal to the shallowest section, see BB.3.1.2 Cn see BB.3.3.2 c is the taper factor defined in BB.3.3.3 BB.3.3 Modification factors for moment gradients in members laterally restrained along the tension flange BB.3.3.1 Linear moment gradients (1)B The modification factor Cm may be determined from Cm = B + B1β t + B 2β t (BB.13) in which B0 = B1 = B2 = η= + 10η + 20η η π + 10 η 0,5 1+ π η − 0,5 + 20η N crE N crT N crE = π EI z Lt L t is the distance between the torsional restraints Š N crT π EI z a π EI w ‹ is the elastic critical torsional buckling force for an I-section GI = 2 + + T 2 is Lt Lt between restraints to both flanges at spacing Lt with intermediate lateral restraints to the tension flange i s2 = i 2y + i 2z + a where a is the distance between the centroid of the member and the centroid of the restraining members, such as purlins restraining rafters 89 91 BS EN 1993-1-1:2005+A1:2014 BS 1993-1-1:2005 ENEN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) βt is the ratio of the algebraically smaller end moment to the larger end moment Moments that produce compression in the non-restrained flange should be taken as positive If the ratio is less than –1,0 the value of βt should be taken as –1,0, see Figure BB.4 + + 200 100 100 – 200 – − 100 βt = = −0,5 + 200 − 200 = −2 + 100 Š but β t ≤ −1,0 thus β t = −1,0 ‹ βt = Figure BB.4: Value of βt BB.3.3.2 Non linear moment gradients (1)B The modification factor Cn may be determined from Cn = 12 [R + 3R + 4R + 3R + R + 2(R S − R E )] (BB.14) in which R1 to R5 are the values of R according to (2)B at the ends, quarter points and mid-length, see Figure BB.5, and only positive values of R should be included In addition, only positive values of (RS – RE) should be included, where – RE is the greater of R1 or R5 – Rs is the maximum value of R anywhere in the length Ly RE RS RE RE R2 R1 R2 R3 R4 R5 R3 R4 R1 RS RS = R E R1 R2 RE R1 R3 R4 R5 R2 R3 R5 ŠFigure BB.5: Moment values ‹ R4 R5 RS (2)B The value of R should be obtained from: R= 90 92 M y ,Ed + a N Ed f y Wpl, y (BB.15) BS EN 1993-1-1:2005+A1:2014 BS EN 1993-1-1:2005 EN 1993-1-1:2005+A1:2014 (E) EN 1993-1-1:2005 (E) where a is the distance between the centroid of the member and the centroid of the restraining members, such as purlins restraining rafters BB.3.3.3 Taper factor (1)B For a non uniform member with constant flanges, for which h ≥ 1,2b and h/tf ≥ 20 the taper factor c should be obtained as follows: – for tapered members or segments, see Figure BB.6(a): h max c = 1+ − 1 h h − tf – 2/3 (BB.16) for haunched members or segments, see Figures BB.6(b) and BB.6(c): hh c = 1+ h s h − tf where hh 2/3 Lh Ly (BB.17) is the additional depth of the haunch or taper, see Figure BB.6; hmax is the maximum depth of cross-section within the length Ly , see Figure BB.6; hmin is the minimum depth of cross-section within the length Ly , see Figure BB.6; hs is the vertical depth of the un-haunched section, see Figure BB.6; Lh is the length of haunch within the length Ly , see Figure BB.6; Ly is the length between points at which the compression flange is laterally restrained (h/tf) is to be derived from the shallowest section h hmax hs hh Ly Lh hs Lh Ly Ly hh (a) Tapered segment (b) Haunched segment (c) Haunched segment x = restraint Figure BB.6: Dimensions defining taper factor 91 93